RESEARCH
Department faculty do fundamental research in classical fields of mathematics and lead the way in newer areas (see Areas of Research below). In addition to intrinsic mathematical research, they collaborate on interdisciplinary projects with Art + Art History + Design, Applied Mathematics, Statistics, Computer Science and Engineering, Bioengineering, Genome Sciences, Electrical Engineering, Mechanical Engineering, Physics, and the Applied Physics Laboratory. Some examples:
- One faculty member has solved a longstanding open problem in the geometry of Riemannian manifolds, showing that knowledge of the distance function on the boundary determines distance overall. This work, featured in Nature, would allow one in principle to determine what is inside an object — the earth for instance — without destroying it.
- Another recently discovered a formula for counting all tanglegrams of a given size. Tanglegrams are combinatorial objects that arise in subjects as varied as the study of cospeciation in biology and analysis of software projects in computer science.
- In work with chemists at UW and beyond, a faculty member solved a probability problem about crystal deposits on a flat surface, thereby providing the theoretical justification for a procedure that may be used for cancer detection.
- To develop a procedure for packing objects of different weights and sizes into the smallest number of boxes in the fastest time, a suitable algorithm will be slow and inefficient. One of our faculty made a major advance by finding an efficient algorithm producing solutions that, if not optimal, are demonstrably close to optimal ones.
Areas of Research
- Algebraic geometry
- Algebraic topology
- Combinatorics
- Complex Analysis
- Differential geometry
- Ergodic Theory and Dynamical Systems
- Inverse Problems
- Noncommutative algebra
- Non-smooth analysis
- Number theory
- Numerical analysis
- Optimization
- Partial differential equations
- Probability
- Representation theory